Subgroups — C₈₉×#35183 #36413031

Order 22784.

1572 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#2866	C₂	1	2	yes	maximal, complemented
2	C₈₉×#2865	C₂	1	2	yes	maximal, complemented
3	C₈₉×#2655	C₂	1	2	yes	maximal, complemented
4	C₈₉×#2651	C₂	1	2	yes	maximal
5	C₈₉×#2596	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2594	C₂	1	2	yes	maximal, complemented
7	C₈₉×#2593	C₂	1	2	yes	maximal
8	C₈₉×#2585	C₂	1	2	yes	maximal, complemented
9	C₈₉×#2570	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#2565	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2562	C₂	1	1	yes	maximal, characteristic
12	C₈₉×#2536	C₂	1	1	yes	maximal, characteristic
13	C₈₉×#2497	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#2494	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#2423	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈₉×#2421	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₉×#2323	C₂	1	1	yes	maximal, characteristic, complemented
18	C₈₉×#2323	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₉×#2314	C₂	1	1	yes	maximal, characteristic, complemented
20	C₈₉×#2314	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#125×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
22	C₈₉×#2293	C₂	1	1	yes	maximal, characteristic
23	C₄²×Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
33	#401×C₈₉	C₂²	1	2	yes	—
34	#400×C₈₉	C₂²	1	2	yes	—
35	#400×C₈₉	C₂²	1	2	yes	—
36	#400×C₈₉	C₂²	1	2	yes	—
37	#400×C₈₉	C₂²	1	2	yes	—
38	#399×C₈₉	C₂²	1	2	yes	—
39	#398×C₈₉	C₂²	1	2	yes	—
40	#398×C₈₉	C₂²	1	2	yes	—
41	#398×C₈₉	C₂²	1	2	yes	—
42	#398×C₈₉	C₂²	1	2	yes	—
43	#398×C₈₉	C₂²	1	2	yes	—
44	#397×C₈₉	C₂²	1	2	yes	—
45	#397×C₈₉	C₂²	1	2	yes	—
46	#396×C₈₉	C₂²	1	2	yes	—
47	#394×C₈₉	C₂²	1	2	yes	—
48	#394×C₈₉	C₂²	1	2	yes	—
49	#391×C₈₉	C₂²	1	1	yes	characteristic
50	#391×C₈₉	C₂²	1	1	yes	characteristic
51	#390×C₈₉	C₂²	1	1	yes	characteristic
52	#390×C₈₉	C₂²	1	1	yes	characteristic
53	#389×C₈₉	C₂²	1	1	yes	characteristic
54	#389×C₈₉	C₂²	1	1	yes	characteristic
55	#389×C₈₉	C₂²	1	1	yes	characteristic
56	#389×C₈₉	C₂²	1	1	yes	characteristic
57	#389×C₈₉	C₂²	1	2	yes	—
58	#389×C₈₉	C₂²	1	2	yes	—
59	#389×C₈₉	C₂²	1	1	yes	characteristic
60	#389×C₈₉	C₂²	1	1	yes	characteristic
61	#388×C₈₉	C₂²	1	2	yes	—
62	#388×C₈₉	C₂²	1	2	yes	—
63	#388×C₈₉	C₂²	1	2	yes	—
64	#388×C₈₉	C₂²	1	2	yes	—
65	#388×C₈₉	C₂²	1	2	yes	—
66	#388×C₈₉	C₂²	1	2	yes	—
67	#388×C₈₉	C₂²	1	2	yes	—
68	#388×C₈₉	C₂²	1	2	yes	—
69	#388×C₈₉	C₂²	1	2	yes	—
70	#388×C₈₉	C₂²	1	2	yes	—
71	#388×C₈₉	C₂²	1	2	yes	—
72	#388×C₈₉	C₂²	1	2	yes	—
73	#388×C₈₉	C₂²	1	2	yes	—
74	#388×C₈₉	C₂²	1	2	yes	—
75	#388×C₈₉	C₂²	1	1	yes	characteristic
76	#388×C₈₉	C₂²	1	2	yes	—
77	#388×C₈₉	C₂²	1	1	yes	characteristic
78	#388×C₈₉	C₂²	1	2	yes	—
79	#388×C₈₉	C₂²	1	1	yes	characteristic
80	#388×C₈₉	C₂²	1	1	yes	characteristic
81	#387×C₈₉	C₂²	1	2	yes	—
82	#387×C₈₉	C₂²	1	2	yes	—
83	#387×C₈₉	C₂²	1	2	yes	—
84	#387×C₈₉	C₂²	1	2	yes	—
85	#387×C₈₉	C₂²	1	2	yes	—
86	#387×C₈₉	C₂²	1	2	yes	—
87	#387×C₈₉	C₂²	1	2	yes	—
88	#387×C₈₉	C₂²	1	2	yes	—
89	#387×C₈₉	C₂²	1	2	yes	—
90	#387×C₈₉	C₂²	1	2	yes	—
91	#387×C₈₉	C₂²	1	2	yes	—
92	#387×C₈₉	C₂²	1	2	yes	—
93	#387×C₈₉	C₂²	1	2	yes	—
94	#387×C₈₉	C₂²	1	2	yes	—
95	#387×C₈₉	C₂²	1	2	yes	—
96	#387×C₈₉	C₂²	1	2	yes	—
97	#384×C₈₉	C₂²	1	1	yes	characteristic
98	#384×C₈₉	C₂²	1	1	yes	characteristic
99	#382×C₈₉	C₂²	1	1	yes	characteristic
100	#382×C₈₉	C₂²	1	1	yes	characteristic
101	#382×C₈₉	C₂²	1	1	yes	characteristic
102	#380×C₈₉	C₂²	1	1	yes	characteristic
103	#380×C₈₉	C₂²	1	1	yes	characteristic
104	#380×C₈₉	C₂²	1	1	yes	characteristic
105	#380×C₈₉	C₂²	1	1	yes	characteristic
106	#380×C₈₉	C₂²	1	1	yes	characteristic
107	#380×C₈₉	C₂²	1	1	yes	characteristic
108	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
109	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
110	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
111	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
112	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
113	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
114	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
115	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
116	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
117	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
118	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
120	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
121	C₄³×C₈₉	C₂²	1	1	yes	characteristic
122	C₄³×C₈₉	C₂²	1	2	yes	—
123	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
124	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
127	#125×C₈₉	—	2	4	no	—
128	C₂²⋊Q₈×C₈₉	—	2	4	no	—
129	C₂²⋊Q₈×C₈₉	—	2	4	no	—
130	C₄×Q₈×C₈₉	—	2	4	no	—
131	C₄×Q₈×C₈₉	—	2	4	no	—
132	C₄×Q₈×C₈₉	—	2	4	no	—
133	C₄×D₄×C₈₉	—	2	4	no	—
134	#117×C₈₉	—	2	4	no	—
135	#117×C₈₉	—	2	4	no	—
136	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
137	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
138	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
139	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
159	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
166	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
167	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
168	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
169	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
170	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
171	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
172	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
173	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
176	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
177	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
183	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
184	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
186	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
187	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
188	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
193	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
194	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
195	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
197	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
198	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
200	#95×C₈₉	C₂³	1	1	yes	characteristic
201	#95×C₈₉	C₂³	1	1	yes	characteristic
202	#95×C₈₉	C₂³	1	1	yes	characteristic
203	#95×C₈₉	C₂³	1	1	yes	characteristic
204	#95×C₈₉	C₂³	1	2	yes	—
205	#95×C₈₉	C₂³	1	2	yes	—
206	#95×C₈₉	C₂³	1	2	yes	—
207	#95×C₈₉	C₂³	1	2	yes	—
208	#95×C₈₉	C₂³	1	2	yes	—
209	#95×C₈₉	C₂³	1	2	yes	—
210	#95×C₈₉	C₂³	1	2	yes	—
211	#95×C₈₉	C₂³	1	1	yes	characteristic
212	#95×C₈₉	C₂³	1	1	yes	characteristic
213	#95×C₈₉	C₂³	1	2	yes	—
214	#95×C₈₉	C₂³	1	2	yes	—
215	#95×C₈₉	C₂³	1	2	yes	—
216	#95×C₈₉	C₂³	1	2	yes	—
217	#95×C₈₉	C₂³	1	2	yes	—
218	#95×C₈₉	C₂³	1	2	yes	—
219	#95×C₈₉	C₂³	1	2	yes	—
220	#95×C₈₉	C₂³	1	2	yes	—
221	#95×C₈₉	C₂³	1	2	yes	—
222	#95×C₈₉	C₂³	1	2	yes	—
223	#95×C₈₉	C₂³	1	2	yes	—
224	#95×C₈₉	C₂³	1	2	yes	—
225	#95×C₈₉	C₂³	1	2	yes	—
226	#95×C₈₉	C₂³	1	2	yes	—
227	#95×C₈₉	C₂³	1	2	yes	—
228	#95×C₈₉	C₂³	1	2	yes	—
229	#95×C₈₉	C₂³	1	2	yes	—
230	#95×C₈₉	C₂³	1	2	yes	—
231	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
232	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
233	C₂×Q₈×C₈₉	—	2	2	no	—
234	C₂×Q₈×C₈₉	—	2	2	no	—
235	C₂×Q₈×C₈₉	#41	1	4	yes	—
236	C₂×D₄×C₈₉	—	2	2	no	—
237	C₂×D₄×C₈₉	—	4	1	no	—
238	C₂×D₄×C₈₉	—	4	1	no	—
239	C₂²×C₄×C₈₉	—	2	2	no	—
240	C₂²×C₄×C₈₉	—	2	2	no	—
241	C₂²×C₄×C₈₉	—	2	2	no	—
242	C₂²×C₄×C₈₉	—	2	2	no	—
243	C₂²×C₄×C₈₉	—	2	2	no	—
244	C₂²×C₄×C₈₉	—	2	2	no	—
245	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
250	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
266	C₄⋊C₄×C₈₉	—	2	2	no	—
267	C₄⋊C₄×C₈₉	—	2	2	no	—
268	C₄⋊C₄×C₈₉	—	2	2	no	—
269	C₄⋊C₄×C₈₉	—	2	2	no	—
270	C₄⋊C₄×C₈₉	—	2	2	no	—
271	C₄⋊C₄×C₈₉	—	2	4	no	—
272	C₄⋊C₄×C₈₉	—	2	4	no	—
273	C₄⋊C₄×C₈₉	—	2	4	no	—
274	C₄⋊C₄×C₈₉	—	2	2	no	—
275	C₄⋊C₄×C₈₉	—	2	2	no	—
276	C₄⋊C₄×C₈₉	—	2	2	no	—
277	C₄⋊C₄×C₈₉	—	2	2	no	—
278	C₄⋊C₄×C₈₉	—	2	2	no	—
279	C₄⋊C₄×C₈₉	—	2	4	no	—
280	C₄⋊C₄×C₈₉	—	2	4	no	—
281	C₄⋊C₄×C₈₉	—	2	4	no	—
282	C₄⋊C₄×C₈₉	—	2	4	no	—
283	C₄⋊C₄×C₈₉	—	2	2	no	—
284	C₄⋊C₄×C₈₉	—	2	2	no	—
285	C₄⋊C₄×C₈₉	—	2	4	no	—
286	C₄⋊C₄×C₈₉	—	4	1	no	—
287	C₄⋊C₄×C₈₉	—	4	1	no	—
288	C₄⋊C₄×C₈₉	—	4	2	no	—
289	C₄⋊C₄×C₈₉	—	4	2	no	—
290	C₄⋊C₄×C₈₉	—	4	2	no	—
291	C₄⋊C₄×C₈₉	—	4	2	no	—
292	C₄⋊C₄×C₈₉	—	4	2	no	—
293	C₄⋊C₄×C₈₉	—	4	2	no	—
294	C₄⋊C₄×C₈₉	—	4	2	no	—
295	C₂²⋊C₄×C₈₉	—	2	2	no	—
296	C₂²⋊C₄×C₈₉	—	2	2	no	—
297	C₂²⋊C₄×C₈₉	—	2	2	no	—
298	C₂²⋊C₄×C₈₉	—	2	2	no	—
299	C₂²⋊C₄×C₈₉	—	2	2	no	—
300	C₂²⋊C₄×C₈₉	—	2	2	no	—
301	C₂²⋊C₄×C₈₉	—	2	4	no	—
302	C₂²⋊C₄×C₈₉	—	2	4	no	—
303	C₂²⋊C₄×C₈₉	—	2	2	no	—
304	C₂²⋊C₄×C₈₉	—	2	2	no	—
305	C₂²⋊C₄×C₈₉	—	4	2	no	—
306	C₂²⋊C₄×C₈₉	—	4	2	no	—
307	C₂²⋊C₄×C₈₉	—	4	1	no	—
308	C₂²⋊C₄×C₈₉	—	4	1	no	—
309	C₂²⋊C₄×C₈₉	—	4	2	no	—
310	C₂²⋊C₄×C₈₉	—	4	2	no	—
311	C₂²⋊C₄×C₈₉	—	4	2	no	—
312	C₂²⋊C₄×C₈₉	—	4	2	no	—
313	C₄²×C₈₉	—	2	2	no	—
314	C₄²×C₈₉	—	2	2	no	—
315	C₄²×C₈₉	—	2	4	no	—
316	C₄²×C₈₉	—	2	2	no	—
317	C₄²×C₈₉	—	2	4	no	—
318	C₄²×C₈₉	—	2	4	no	—
319	C₄²×C₈₉	—	2	2	no	—
320	C₄²×C₈₉	—	4	1	no	—
321	C₄²×C₈₉	—	4	1	no	—
322	C₄²×C₈₉	—	4	1	no	—
323	C₄²×C₈₉	—	4	2	no	—
324	C₄²×C₈₉	—	4	2	no	—
325	C₄²×C₈₉	—	4	2	no	—
326	C₄²×C₈₉	—	4	2	no	—
327	C₄²×C₈₉	—	4	2	no	—
328	C₄²×C₈₉	#41	1	4	yes	—
329	C₄²×C₈₉	#41	1	4	yes	—
330	C₂³×C₈₉	—	2	1	no	—
331	C₂³×C₈₉	—	2	1	no	—
332	C₂³×C₈₉	—	2	1	no	—
333	C₂³×C₈₉	—	2	1	no	—
334	C₂³×C₈₉	—	2	1	no	—
335	C₂³×C₈₉	—	2	1	no	—
336	C₂³×C₈₉	—	2	1	no	—
337	C₂³×C₈₉	—	2	1	no	—
338	C₂³×C₈₉	—	2	1	no	—
339	C₂³×C₈₉	—	2	1	no	—
340	C₂³×C₈₉	—	2	1	no	—
341	C₂³×C₈₉	—	2	1	no	—
342	C₂³×C₈₉	—	2	1	no	—
343	C₂³×C₈₉	—	2	1	no	—
344	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
345	Q₈×C₈₉	—	2	8	no	—
346	D₄×C₈₉	—	4	4	no	—
347	C₂×C₄×C₈₉	—	2	1	no	—
348	C₂×C₄×C₈₉	—	2	2	no	—
349	C₂×C₄×C₈₉	—	2	2	no	—
350	C₂×C₄×C₈₉	—	2	1	no	—
351	C₂×C₄×C₈₉	—	2	1	no	—
352	C₂×C₄×C₈₉	—	2	1	no	—
353	C₂×C₄×C₈₉	—	2	1	no	—
354	C₂×C₄×C₈₉	—	2	1	no	—
355	C₂×C₄×C₈₉	—	2	1	no	—
356	C₂×C₄×C₈₉	—	2	1	no	—
357	C₂×C₄×C₈₉	—	2	1	no	—
358	C₂×C₄×C₈₉	—	2	1	no	—
359	C₂×C₄×C₈₉	—	2	1	no	—
360	C₂×C₄×C₈₉	—	2	1	no	—
361	C₂×C₄×C₈₉	—	2	1	no	—
362	C₂×C₄×C₈₉	—	2	1	no	—
363	C₂×C₄×C₈₉	—	2	2	no	—
364	C₂×C₄×C₈₉	—	2	2	no	—
365	C₂×C₄×C₈₉	—	2	1	no	—
366	C₂×C₄×C₈₉	—	2	2	no	—
367	C₂×C₄×C₈₉	—	2	2	no	—
368	C₂×C₄×C₈₉	—	2	2	no	—
369	C₂×C₄×C₈₉	—	2	1	no	—
370	C₂×C₄×C₈₉	—	2	1	no	—
371	C₂×C₄×C₈₉	—	2	2	no	—
372	C₂×C₄×C₈₉	—	2	2	no	—
373	C₂×C₄×C₈₉	—	2	1	no	—
374	C₂×C₄×C₈₉	—	2	1	no	—
375	C₂×C₄×C₈₉	—	2	1	no	—
376	C₂×C₄×C₈₉	—	2	1	no	—
377	C₂×C₄×C₈₉	—	2	1	no	—
378	C₂×C₄×C₈₉	—	2	1	no	—
379	C₂×C₄×C₈₉	—	2	2	no	—
380	C₂×C₄×C₈₉	—	2	2	no	—
381	C₂×C₄×C₈₉	—	2	2	no	—
382	C₂×C₄×C₈₉	—	2	1	no	—
383	C₂×C₄×C₈₉	—	2	2	no	—
384	C₂×C₄×C₈₉	—	2	2	no	—
385	C₂×C₄×C₈₉	—	2	2	no	—
386	C₂×C₄×C₈₉	—	2	2	no	—
387	C₂×C₄×C₈₉	—	2	2	no	—
388	C₂×C₄×C₈₉	—	2	2	no	—
389	C₂×C₄×C₈₉	—	2	2	no	—
390	C₂×C₄×C₈₉	—	2	2	no	—
391	C₂×C₄×C₈₉	—	2	1	no	—
392	C₂×C₄×C₈₉	—	2	2	no	—
393	C₂×C₄×C₈₉	—	2	2	no	—
394	C₂×C₄×C₈₉	—	2	1	no	—
395	C₂×C₄×C₈₉	—	2	1	no	—
396	C₂×C₄×C₈₉	—	2	2	no	—
397	C₂×C₄×C₈₉	—	2	1	no	—
398	C₂×C₄×C₈₉	—	2	1	no	—
399	C₂×C₄×C₈₉	—	2	1	no	—
400	C₂×C₄×C₈₉	—	2	1	no	—
401	C₂×C₄×C₈₉	—	4	4	no	—
402	C₂×C₄×C₈₉	—	4	4	no	—
403	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
404	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
405	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
406	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
407	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
408	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
409	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
410	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
411	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
412	C₂²×C₈₉	—	4	1	no	—
413	C₂²×C₈₉	—	4	1	no	—
414	C₂²×C₈₉	—	4	1	no	—
415	C₂²×C₈₉	—	4	1	no	—
416	C₂²×C₈₉	—	4	1	no	—
417	C₂²×C₈₉	—	4	1	no	—
418	C₂²×C₈₉	—	4	1	no	—
419	C₂²×C₈₉	—	4	1	no	—
420	C₂²×C₈₉	—	4	1	no	—
421	C₂²×C₈₉	—	4	1	no	—
422	C₂²×C₈₉	—	4	1	no	—
423	C₂²×C₈₉	—	4	1	no	—
424	C₂²×C₈₉	—	4	1	no	—
425	C₂²×C₈₉	—	4	1	no	—
426	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
427	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
428	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
429	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
430	C₂²×C₈₉	#585	1	1	yes	characteristic
431	C₂²×C₈₉	#585	1	1	yes	characteristic
432	C₂²×C₈₉	#585	1	1	yes	characteristic
433	C₄×C₈₉	—	2	4	no	—
434	C₄×C₈₉	—	2	2	no	—
435	C₄×C₈₉	—	2	2	no	—
436	C₄×C₈₉	—	2	2	no	—
437	C₄×C₈₉	—	2	2	no	—
438	C₄×C₈₉	—	2	2	no	—
439	C₄×C₈₉	—	4	1	no	—
440	C₄×C₈₉	—	4	1	no	—
441	C₄×C₈₉	—	4	2	no	—
442	C₄×C₈₉	—	4	2	no	—
443	C₄×C₈₉	—	4	2	no	—
444	C₄×C₈₉	—	4	1	no	—
445	C₄×C₈₉	—	4	1	no	—
446	C₄×C₈₉	—	4	1	no	—
447	C₄×C₈₉	—	4	1	no	—
448	C₄×C₈₉	—	4	2	no	—
449	C₄×C₈₉	—	4	2	no	—
450	C₄×C₈₉	—	4	1	no	—
451	C₄×C₈₉	—	4	2	no	—
452	C₄×C₈₉	—	4	2	no	—
453	C₄×C₈₉	#529	1	4	yes	—
454	#35183	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
455	C₂×C₈₉	—	8	1	no	—
456	C₂×C₈₉	—	8	1	no	—
457	C₂×C₈₉	C₂×#529	1	1	yes	characteristic
458	C₂×C₈₉	#3455	1	1	yes	characteristic
459	C₂×C₈₉	#3461	1	1	yes	characteristic
460	C₂×C₈₉	#3507	1	1	yes	characteristic
461	C₂×C₈₉	#3512	1	1	yes	characteristic
462	C₂×C₈₉	#3516	1	1	yes	characteristic
463	C₂×C₈₉	#3524	1	1	yes	characteristic
464	#2866	C₂×C₈₉	1	2	yes	complemented
465	#2865	C₂×C₈₉	1	2	yes	complemented
466	#2655	C₂×C₈₉	1	2	yes	complemented
467	#2651	C₂×C₈₉	1	2	yes	—
468	#2596	C₂×C₈₉	1	2	yes	complemented
469	#2594	C₂×C₈₉	1	2	yes	complemented
470	#2593	C₂×C₈₉	1	2	yes	—
471	#2585	C₂×C₈₉	1	2	yes	complemented
472	#2570	C₂×C₈₉	1	1	yes	characteristic, complemented
473	#2565	C₂×C₈₉	1	1	yes	characteristic, complemented
474	#2562	C₂×C₈₉	1	1	yes	characteristic
475	#2536	C₂×C₈₉	1	1	yes	characteristic
476	#2497	C₂×C₈₉	1	1	yes	characteristic, complemented
477	#2494	C₂×C₈₉	1	1	yes	characteristic, complemented
478	#2423	C₂×C₈₉	1	1	yes	characteristic, complemented
479	#2421	C₂×C₈₉	1	1	yes	characteristic, complemented
480	#2323	C₂×C₈₉	1	1	yes	characteristic, complemented
481	#2323	C₂×C₈₉	1	1	yes	characteristic, complemented
482	#2314	C₂×C₈₉	1	1	yes	characteristic, complemented
483	#2314	C₂×C₈₉	1	1	yes	characteristic, complemented
484	C₄×#125	C₂×C₈₉	1	1	yes	characteristic, complemented
485	#2293	C₂×C₈₉	1	1	yes	characteristic
486	C₄²×Q₈	C₂×C₈₉	1	1	yes	characteristic, complemented
487	C₈₉	#35183	1	1	yes	characteristic, direct product factor, Sylow
488	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic
489	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
490	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
491	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
492	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
493	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
494	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
495	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
496	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
497	#401	C₂²×C₈₉	1	2	yes	—
498	#400	C₂²×C₈₉	1	2	yes	—
499	#400	C₂²×C₈₉	1	2	yes	—
500	#400	C₂²×C₈₉	1	2	yes	—
501	#400	C₂²×C₈₉	1	2	yes	—
502	#399	C₂²×C₈₉	1	2	yes	—
503	#398	C₂²×C₈₉	1	2	yes	—
504	#398	C₂²×C₈₉	1	2	yes	—
505	#398	C₂²×C₈₉	1	2	yes	—
506	#398	C₂²×C₈₉	1	2	yes	—
507	#398	C₂²×C₈₉	1	2	yes	—
508	#397	C₂²×C₈₉	1	2	yes	—
509	#397	C₂²×C₈₉	1	2	yes	—
510	#396	C₂²×C₈₉	1	2	yes	—
511	#394	C₂²×C₈₉	1	2	yes	—
512	#394	C₂²×C₈₉	1	2	yes	—
513	#391	C₂²×C₈₉	1	1	yes	characteristic
514	#391	C₂²×C₈₉	1	1	yes	characteristic
515	#390	C₂²×C₈₉	1	1	yes	characteristic
516	#390	C₂²×C₈₉	1	1	yes	characteristic
517	#389	C₂²×C₈₉	1	1	yes	characteristic
518	#389	C₂²×C₈₉	1	1	yes	characteristic
519	#389	C₂²×C₈₉	1	1	yes	characteristic
520	#389	C₂²×C₈₉	1	1	yes	characteristic
521	#389	C₂²×C₈₉	1	2	yes	—
522	#389	C₂²×C₈₉	1	2	yes	—
523	#389	C₂²×C₈₉	1	1	yes	characteristic
524	#389	C₂²×C₈₉	1	1	yes	characteristic
525	#388	C₂²×C₈₉	1	2	yes	—
526	#388	C₂²×C₈₉	1	2	yes	—
527	#388	C₂²×C₈₉	1	2	yes	—
528	#388	C₂²×C₈₉	1	2	yes	—
529	#388	C₂²×C₈₉	1	2	yes	—
530	#388	C₂²×C₈₉	1	2	yes	—
531	#388	C₂²×C₈₉	1	2	yes	—
532	#388	C₂²×C₈₉	1	2	yes	—
533	#388	C₂²×C₈₉	1	2	yes	—
534	#388	C₂²×C₈₉	1	2	yes	—
535	#388	C₂²×C₈₉	1	2	yes	—
536	#388	C₂²×C₈₉	1	2	yes	—
537	#388	C₂²×C₈₉	1	2	yes	—
538	#388	C₂²×C₈₉	1	2	yes	—
539	#388	C₂²×C₈₉	1	1	yes	characteristic
540	#388	C₂²×C₈₉	1	2	yes	—
541	#388	C₂²×C₈₉	1	1	yes	characteristic
542	#388	C₂²×C₈₉	1	2	yes	—
543	#388	C₂²×C₈₉	1	1	yes	characteristic
544	#388	C₂²×C₈₉	1	1	yes	characteristic
545	#387	C₂²×C₈₉	1	2	yes	—
546	#387	C₂²×C₈₉	1	2	yes	—
547	#387	C₂²×C₈₉	1	2	yes	—
548	#387	C₂²×C₈₉	1	2	yes	—
549	#387	C₂²×C₈₉	1	2	yes	—
550	#387	C₂²×C₈₉	1	2	yes	—
551	#387	C₂²×C₈₉	1	2	yes	—
552	#387	C₂²×C₈₉	1	2	yes	—
553	#387	C₂²×C₈₉	1	2	yes	—
554	#387	C₂²×C₈₉	1	2	yes	—
555	#387	C₂²×C₈₉	1	2	yes	—
556	#387	C₂²×C₈₉	1	2	yes	—
557	#387	C₂²×C₈₉	1	2	yes	—
558	#387	C₂²×C₈₉	1	2	yes	—
559	#387	C₂²×C₈₉	1	2	yes	—
560	#387	C₂²×C₈₉	1	2	yes	—
561	#384	C₂²×C₈₉	1	1	yes	characteristic
562	#384	C₂²×C₈₉	1	1	yes	characteristic
563	#382	C₂²×C₈₉	1	1	yes	characteristic
564	#382	C₂²×C₈₉	1	1	yes	characteristic
565	#382	C₂²×C₈₉	1	1	yes	characteristic
566	#380	C₂²×C₈₉	1	1	yes	characteristic
567	#380	C₂²×C₈₉	1	1	yes	characteristic
568	#380	C₂²×C₈₉	1	1	yes	characteristic
569	#380	C₂²×C₈₉	1	1	yes	characteristic
570	#380	C₂²×C₈₉	1	1	yes	characteristic
571	#380	C₂²×C₈₉	1	1	yes	characteristic
572	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
573	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
574	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
575	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
576	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
577	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
578	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
579	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
580	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
581	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
582	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
583	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
584	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
585	C₄³	C₂²×C₈₉	1	1	yes	characteristic
586	C₄³	C₂²×C₈₉	1	2	yes	—
587	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
588	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
589	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
590	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
591	#125	—	2	4	no	—
592	C₂²⋊Q₈	—	2	4	no	—
593	C₂²⋊Q₈	—	2	4	no	—
594	C₄×Q₈	—	2	4	no	—
595	C₄×Q₈	—	2	4	no	—
596	C₄×Q₈	—	2	4	no	—
597	C₄×D₄	—	2	4	no	—
598	#117	—	2	4	no	—
599	#117	—	2	4	no	—
600	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
601	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
602	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
604	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
606	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
607	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
608	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
609	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
610	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
611	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
612	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
613	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
614	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
615	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
616	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
617	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
618	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
619	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
620	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
621	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
622	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
623	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
624	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
625	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
626	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
627	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
628	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
629	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
630	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
631	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
632	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
633	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
634	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
635	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
636	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
637	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
638	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
639	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
640	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
641	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
642	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
643	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
644	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
645	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
646	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
647	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
648	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
649	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
650	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
651	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
652	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
653	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
654	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
655	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
656	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
657	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
658	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
659	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
660	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
661	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
662	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
663	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
664	#95	C₂³×C₈₉	1	1	yes	characteristic
665	#95	C₂³×C₈₉	1	1	yes	characteristic
666	#95	C₂³×C₈₉	1	1	yes	characteristic
667	#95	C₂³×C₈₉	1	1	yes	characteristic
668	#95	C₂³×C₈₉	1	2	yes	—
669	#95	C₂³×C₈₉	1	2	yes	—
670	#95	C₂³×C₈₉	1	2	yes	—
671	#95	C₂³×C₈₉	1	2	yes	—
672	#95	C₂³×C₈₉	1	2	yes	—
673	#95	C₂³×C₈₉	1	2	yes	—
674	#95	C₂³×C₈₉	1	2	yes	—
675	#95	C₂³×C₈₉	1	1	yes	characteristic
676	#95	C₂³×C₈₉	1	1	yes	characteristic
677	#95	C₂³×C₈₉	1	2	yes	—
678	#95	C₂³×C₈₉	1	2	yes	—
679	#95	C₂³×C₈₉	1	2	yes	—
680	#95	C₂³×C₈₉	1	2	yes	—
681	#95	C₂³×C₈₉	1	2	yes	—
682	#95	C₂³×C₈₉	1	2	yes	—
683	#95	C₂³×C₈₉	1	2	yes	—
684	#95	C₂³×C₈₉	1	2	yes	—
685	#95	C₂³×C₈₉	1	2	yes	—
686	#95	C₂³×C₈₉	1	2	yes	—
687	#95	C₂³×C₈₉	1	2	yes	—
688	#95	C₂³×C₈₉	1	2	yes	—
689	#95	C₂³×C₈₉	1	2	yes	—
690	#95	C₂³×C₈₉	1	2	yes	—
691	#95	C₂³×C₈₉	1	2	yes	—
692	#95	C₂³×C₈₉	1	2	yes	—
693	#95	C₂³×C₈₉	1	2	yes	—
694	#95	C₂³×C₈₉	1	2	yes	—
695	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
696	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
697	C₂×Q₈	—	2	2	no	—
698	C₂×Q₈	—	2	2	no	—
699	C₂×Q₈	#41×C₈₉	1	4	yes	—
700	C₂×D₄	—	2	2	no	—
701	C₂×D₄	—	4	1	no	—
702	C₂×D₄	—	4	1	no	—
703	C₂²×C₄	—	2	2	no	—
704	C₂²×C₄	—	2	2	no	—
705	C₂²×C₄	—	2	2	no	—
706	C₂²×C₄	—	2	2	no	—
707	C₂²×C₄	—	2	2	no	—
708	C₂²×C₄	—	2	2	no	—
709	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
710	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
711	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
712	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
713	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
714	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
715	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
716	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
717	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
718	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
719	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
720	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
721	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
722	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
723	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
724	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
725	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
726	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
727	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
728	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
729	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	4	no	—
736	C₄⋊C₄	—	2	4	no	—
737	C₄⋊C₄	—	2	4	no	—
738	C₄⋊C₄	—	2	2	no	—
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	4	no	—
744	C₄⋊C₄	—	2	4	no	—
745	C₄⋊C₄	—	2	4	no	—
746	C₄⋊C₄	—	2	4	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	2	no	—
749	C₄⋊C₄	—	2	4	no	—
750	C₄⋊C₄	—	4	1	no	—
751	C₄⋊C₄	—	4	1	no	—
752	C₄⋊C₄	—	4	2	no	—
753	C₄⋊C₄	—	4	2	no	—
754	C₄⋊C₄	—	4	2	no	—
755	C₄⋊C₄	—	4	2	no	—
756	C₄⋊C₄	—	4	2	no	—
757	C₄⋊C₄	—	4	2	no	—
758	C₄⋊C₄	—	4	2	no	—
759	C₂²⋊C₄	—	2	2	no	—
760	C₂²⋊C₄	—	2	2	no	—
761	C₂²⋊C₄	—	2	2	no	—
762	C₂²⋊C₄	—	2	2	no	—
763	C₂²⋊C₄	—	2	2	no	—
764	C₂²⋊C₄	—	2	2	no	—
765	C₂²⋊C₄	—	2	4	no	—
766	C₂²⋊C₄	—	2	4	no	—
767	C₂²⋊C₄	—	2	2	no	—
768	C₂²⋊C₄	—	2	2	no	—
769	C₂²⋊C₄	—	4	2	no	—
770	C₂²⋊C₄	—	4	2	no	—
771	C₂²⋊C₄	—	4	1	no	—
772	C₂²⋊C₄	—	4	1	no	—
773	C₂²⋊C₄	—	4	2	no	—
774	C₂²⋊C₄	—	4	2	no	—
775	C₂²⋊C₄	—	4	2	no	—
776	C₂²⋊C₄	—	4	2	no	—
777	C₄²	—	2	2	no	—
778	C₄²	—	2	2	no	—
779	C₄²	—	2	4	no	—
780	C₄²	—	2	2	no	—
781	C₄²	—	2	4	no	—
782	C₄²	—	2	4	no	—
783	C₄²	—	2	2	no	—
784	C₄²	—	4	1	no	—
785	C₄²	—	4	1	no	—
786	C₄²	—	4	1	no	—
787	C₄²	—	4	2	no	—
788	C₄²	—	4	2	no	—
789	C₄²	—	4	2	no	—
790	C₄²	—	4	2	no	—
791	C₄²	—	4	2	no	—
792	C₄²	#41×C₈₉	1	4	yes	—
793	C₄²	#41×C₈₉	1	4	yes	—
794	C₂³	—	2	1	no	—
795	C₂³	—	2	1	no	—
796	C₂³	—	2	1	no	—
797	C₂³	—	2	1	no	—
798	C₂³	—	2	1	no	—
799	C₂³	—	2	1	no	—
800	C₂³	—	2	1	no	—
801	C₂³	—	2	1	no	—
802	C₂³	—	2	1	no	—
803	C₂³	—	2	1	no	—
804	C₂³	—	2	1	no	—
805	C₂³	—	2	1	no	—
806	C₂³	—	2	1	no	—
807	C₂³	—	2	1	no	—
808	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
809	Q₈	—	2	8	no	—
810	D₄	—	4	4	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	1	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	4	4	no	—
866	C₂×C₄	—	4	4	no	—
867	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
868	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
869	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
870	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
871	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
872	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
873	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
874	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
875	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
876	C₂²	—	4	1	no	—
877	C₂²	—	4	1	no	—
878	C₂²	—	4	1	no	—
879	C₂²	—	4	1	no	—
880	C₂²	—	4	1	no	—
881	C₂²	—	4	1	no	—
882	C₂²	—	4	1	no	—
883	C₂²	—	4	1	no	—
884	C₂²	—	4	1	no	—
885	C₂²	—	4	1	no	—
886	C₂²	—	4	1	no	—
887	C₂²	—	4	1	no	—
888	C₂²	—	4	1	no	—
889	C₂²	—	4	1	no	—
890	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
891	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
892	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
893	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
894	C₂²	#585×C₈₉	1	1	yes	characteristic
895	C₂²	#585×C₈₉	1	1	yes	characteristic
896	C₂²	#585×C₈₉	1	1	yes	characteristic
897	C₄	—	2	4	no	—
898	C₄	—	2	2	no	—
899	C₄	—	2	2	no	—
900	C₄	—	2	2	no	—
901	C₄	—	2	2	no	—
902	C₄	—	2	2	no	—
903	C₄	—	4	1	no	—
904	C₄	—	4	1	no	—
905	C₄	—	4	2	no	—
906	C₄	—	4	2	no	—
907	C₄	—	4	2	no	—
908	C₄	—	4	1	no	—
909	C₄	—	4	1	no	—
910	C₄	—	4	1	no	—
911	C₄	—	4	1	no	—
912	C₄	—	4	2	no	—
913	C₄	—	4	2	no	—
914	C₄	—	4	1	no	—
915	C₄	—	4	2	no	—
916	C₄	—	4	2	no	—
917	C₄	#529×C₈₉	1	4	yes	—
918	C₂	—	8	1	no	—
919	C₂	—	8	1	no	—
920	C₂	C₂×#529×C₈₉	1	1	yes	characteristic
921	C₂	C₈₉×#3455	1	1	yes	characteristic
922	C₂	C₈₉×#3461	1	1	yes	characteristic
923	C₂	C₈₉×#3507	1	1	yes	characteristic
924	C₂	C₈₉×#3512	1	1	yes	characteristic
925	C₂	C₈₉×#3516	1	1	yes	characteristic
926	C₂	C₈₉×#3524	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂²×D₄×C₈₉	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₈₉×#2866	C₂	semidirect
2. C₈₉×#2865	C₂	semidirect
3. C₈₉×#2655	C₂	semidirect
5. C₈₉×#2596	C₂	semidirect
6. C₈₉×#2594	C₂	semidirect
8. C₈₉×#2585	C₂	semidirect
9. C₈₉×#2570	C₂	semidirect
10. C₈₉×#2565	C₂	semidirect
13. C₈₉×#2497	C₂	semidirect
14. C₈₉×#2494	C₂	semidirect
15. C₈₉×#2423	C₂	semidirect
16. C₈₉×#2421	C₂	semidirect
17. C₈₉×#2323	C₂	semidirect
18. C₈₉×#2323	C₂	semidirect
19. C₈₉×#2314	C₂	semidirect
20. C₈₉×#2314	C₂	semidirect
21. C₄×#125×C₈₉	C₂	semidirect
23. C₄²×Q₈×C₈₉	C₂	semidirect
454. #35183	C₈₉	direct (N × H)
464. #2866	C₂×C₈₉	semidirect
465. #2865	C₂×C₈₉	semidirect
466. #2655	C₂×C₈₉	semidirect
468. #2596	C₂×C₈₉	semidirect
469. #2594	C₂×C₈₉	semidirect
471. #2585	C₂×C₈₉	semidirect
472. #2570	C₂×C₈₉	semidirect
473. #2565	C₂×C₈₉	semidirect
476. #2497	C₂×C₈₉	semidirect
477. #2494	C₂×C₈₉	semidirect
478. #2423	C₂×C₈₉	semidirect
479. #2421	C₂×C₈₉	semidirect
480. #2323	C₂×C₈₉	semidirect
481. #2323	C₂×C₈₉	semidirect
482. #2314	C₂×C₈₉	semidirect
483. #2314	C₂×C₈₉	semidirect
484. C₄×#125	C₂×C₈₉	semidirect
486. C₄²×Q₈	C₂×C₈₉	semidirect
487. C₈₉	#35183	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₈₉×#2866	2
C₈₉×#2865	2
C₈₉×#2655	2
C₈₉×#2651	2
C₈₉×#2596	2
C₈₉×#2594	2
C₈₉×#2593	2
C₈₉×#2585	2
C₈₉×#2570	2
C₈₉×#2565	2
C₈₉×#2562	2
C₈₉×#2536	2
C₈₉×#2497	2
C₈₉×#2494	2
C₈₉×#2423	2
C₈₉×#2421	2
C₈₉×#2323	2
C₈₉×#2314	2
C₄×#125×C₈₉	2
C₈₉×#2293	2
C₄²×Q₈×C₈₉	2
#35183	89

Subgroups — C89×#35183 #36413031

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35183 #36413031